Thermalization in Krylov basis
Abstract We study thermalization in closed non-integrable quantum systems using the Krylov basis. We demonstrate that for thermalization to occur, the matrix representation of typical local operators in the Krylov basis should exhibit a specific tridiagonal form with all other elements in the matrix...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-01-01
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| Series: | European Physical Journal C: Particles and Fields |
| Online Access: | https://doi.org/10.1140/epjc/s10052-025-13757-2 |
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| _version_ | 1832585449592324096 |
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| author | Mohsen Alishahiha Mohammad Javad Vasli |
| author_facet | Mohsen Alishahiha Mohammad Javad Vasli |
| author_sort | Mohsen Alishahiha |
| collection | DOAJ |
| description | Abstract We study thermalization in closed non-integrable quantum systems using the Krylov basis. We demonstrate that for thermalization to occur, the matrix representation of typical local operators in the Krylov basis should exhibit a specific tridiagonal form with all other elements in the matrix being exponentially small, reminiscent of the eigenstate thermalization hypothesis. Within this framework, we propose that the nature of thermalization, whether weak or strong, can be examined by the infinite time average of the Krylov complexity. Moreover, we analyze the variance of Lanczos coefficients as another probe for the nature of thermalization. One observes that although the variance of Lanczos coefficients may capture certain features of thermalization, it is not as effective as the infinite time average of complexity. |
| format | Article |
| id | doaj-art-b8df8ad795fd4f3b9f5fceed8873f11e |
| institution | Kabale University |
| issn | 1434-6052 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | European Physical Journal C: Particles and Fields |
| spelling | doaj-art-b8df8ad795fd4f3b9f5fceed8873f11e2025-01-26T12:49:33ZengSpringerOpenEuropean Physical Journal C: Particles and Fields1434-60522025-01-0185111610.1140/epjc/s10052-025-13757-2Thermalization in Krylov basisMohsen Alishahiha0Mohammad Javad Vasli1School of Physics, Institute for Research in Fundamental Sciences (IPM)School of Physics, Institute for Research in Fundamental Sciences (IPM)Abstract We study thermalization in closed non-integrable quantum systems using the Krylov basis. We demonstrate that for thermalization to occur, the matrix representation of typical local operators in the Krylov basis should exhibit a specific tridiagonal form with all other elements in the matrix being exponentially small, reminiscent of the eigenstate thermalization hypothesis. Within this framework, we propose that the nature of thermalization, whether weak or strong, can be examined by the infinite time average of the Krylov complexity. Moreover, we analyze the variance of Lanczos coefficients as another probe for the nature of thermalization. One observes that although the variance of Lanczos coefficients may capture certain features of thermalization, it is not as effective as the infinite time average of complexity.https://doi.org/10.1140/epjc/s10052-025-13757-2 |
| spellingShingle | Mohsen Alishahiha Mohammad Javad Vasli Thermalization in Krylov basis European Physical Journal C: Particles and Fields |
| title | Thermalization in Krylov basis |
| title_full | Thermalization in Krylov basis |
| title_fullStr | Thermalization in Krylov basis |
| title_full_unstemmed | Thermalization in Krylov basis |
| title_short | Thermalization in Krylov basis |
| title_sort | thermalization in krylov basis |
| url | https://doi.org/10.1140/epjc/s10052-025-13757-2 |
| work_keys_str_mv | AT mohsenalishahiha thermalizationinkrylovbasis AT mohammadjavadvasli thermalizationinkrylovbasis |